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#### State Estimation Theory of Networked Control Systems

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Chapter 1 Data-Rate Theorem for Networked Control Systems 1
1．1 Linear Discrete-Time Systems 1
1．1．1 Introduction 1
1．1．2 Problem Formulation 4
1．1．3 State Estimation under Data-Rate Limitations 5
1．1．4 Numerical Examples and Simulations 19
1．2 Linear Continuous Time-Invariant Systems 21
1．2．1 Introduction 22
1．2．2 Problem Formulation 23
1．2．3 State Estimation under Information Limitations 24
1．2．4 Numerical Examples and Simulations 26
References 28
Chapter 2 Coding Schemes for Observability and Stabilizability under
Data-Rate Limitations 31
2．1 Variable-Length Coding 31
2．1．1 Introduction 31
2．1．2 Problem Formulation 33
2．1．3 Quantization， Coding and Control Schemes 35
2．1．4 Sufficient Conditions for Observability and Stabilizability 40
2．1．5 Numerical Examples and Simulations 50
2．2 Fixed-Length Coding 53
2．2．1 Introduction 53
2．2．2 Problem Formulation 54
2．2．3 Quantization and Coding 55
2．2．4 Numerical Examples and Simulations 61
2．3 Time-Varying Coding 62
2．3．1 Introduction 63
2．3．2 Problem Formulation 64
2．3．3 Quantization and Coding 65
2．3．4 Numerical Examples and Simulations 72
References 74
Chapter 3 State Estimation under Data-Rate Limitations 78
3．1 Scalar Linear Continuous Time-Invariant Systems 78
3．1．1 Introduction 78
3．1．2 Problem Formulation 79
3．1．3 Conditions on the Constant Data Rate for Observability 80
3．1．4 Numerical Examples and Simulations 83
3．2 Multi-Input Multi-Output Linear Systems 85
3．2．1 Introduction 85
3．2．2 Problem Formulation 86
3．2．3 Conditions on the Constant Data Rate for Observability 88
3．2．4 Numerical Examples and Simulations 91
3．3 Jordan Canonical Form of System Matrix 93
3．3．1 Introduction 93
3．3．2 Problem Formulation 94
3．3．3 A Lower Bound on the Data Rate for Observability 96
3．4 Linear Discrete-Time Systems with Extreme Data-Rate Limitations 100
3．4．1 Introduction 100
3．4．2 Problem Formulation 101
3．4．3 Optimal Encoder and Decoder Design 102
3．4．4 Numerical Examples and Simulations 105
3．5 Linear Continuous-Time Systems with Extreme Data-Rate Limitations 106
3．5．1 Introduction 107
3．5．2 Problem Formulation 108
3．5．3 Conditions for Observability 109
3．5．4 Numerical Examples and Simulations 112
References 113
Chapter 4 Observability and Stabilizability of Linear Systems with Time
Delays 117
4．1 Systems with Random Time Delays 117
4．1．1 Introduction 117
4．1．2 Problem Formulation 119
4．1．3 State Estimation over Channels with Random Time Delays 120
4．1．4 Numerical Examples and Simulations 124
4．2 Systems with Random Time Delays and Limited Data-Rates 126
4．2．1 Introduction 126
4．2．2 Problem Formulation 127
4．2．3 Optimal Encoder and Decoder Design 130
4．2．4 Conditions for Observability 132
4．2．5 Numerical Examples and Simulations 142
4．3 Systems with Fixed Time Delay 146
4．3．1 Introduction 146
4．3．2 Problem Formulation 147
4．3．3 Control under Communication Constraints 148
4．3．4 Numerical Examples and Simulations 152
References 154
Chapter 5 State Estimation over Limited Capacity and Dropout Channels 158
5．1 Observability over an AWGN Channel 158
5．1．1 Introduction 158
5．1．2 Problem Formulation 159
5．1．3 State Estimation over AWGN Channels 160
5．1．4 Numerical Examples and Simulations 163
5．2 Observability under Packet Dropout and Time Delay 165
5．2．1 Introduction 165
5．2．2 Problem Formulation 166
5．2．3 Sufficient Conditions for Observability 167
5．2．4 Numerical Examples and Simulations 170
References 173
Chapter 6 Linear Quadratic Control for Networked Control Systems with
Information Limitations 176
6．1 LQ Cost for Plant States 176
6．1．1 Introduction 176
6．1．2 Problem Formulation 177
6．1．3 LQ Control under Information Limitations 178
6．2 LQ Cost for Plant States and Control Inputs 184
6．2．1 Introduction 184
6．2．2 Problem Formulation 186
6．2．3 Control Scheme under Information Rate Limitations 186
6．2．4 Numerical Examples and Simulations 190
References 192
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